DLMF:11.6.E2 (Q3978)

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DLMF:11.6.E2
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    Statements

    Defining formula
    𝐌 ν ⁡ ( z ) ∼ 1 π ⁢ ∑ k = 0 ∞ ( - 1 ) k + 1 ⁢ Γ ⁡ ( k + 1 2 ) ⁢ ( 1 2 ⁢ z ) ν - 2 ⁢ k - 1 Γ ⁡ ( ν + 1 2 - k ) , asymptotic-expansion associated-Struve-M 𝜈 𝑧 1 𝜋 superscript subscript 𝑘 0 superscript 1 𝑘 1 Euler-Gamma 𝑘 1 2 superscript 1 2 𝑧 𝜈 2 𝑘 1 Euler-Gamma 𝜈 1 2 𝑘 {\displaystyle{\displaystyle\mathbf{M}_{\nu}\left(z\right)\sim\frac{1}{\pi}% \sum_{k=0}^{\infty}(-1)^{k+1}\frac{\Gamma\left(k+\tfrac{1}{2}\right)(\tfrac{1}% {2}z)^{\nu-2k-1}}{\Gamma\left(\nu+\tfrac{1}{2}-k\right)},}}
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    DLMF id
    DLMF:11.6.E2
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    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}
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